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Register a new userHolographic Ward identities for symmetry breaking in two dimensions
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We investigate symmetry breaking in two-dimensional field theories which have a holographic gravity dual. Being at large N, the Coleman theorem does not hold and Goldstone bosons are expected. We consider the minimal setup to describe a conserved current and a charged operator, and we perform holographic renormalization in order to find the correct Ward identities describing symmetry breaking. This involves some subtleties related to the different boundary conditions that a vector can have in the three-dimensional bulk. We establish which is the correct prescription that yields, after renormalization, the same Ward identities as in higher dimensions.
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We consider finite superamplitudes of N=1 matter, and use superconformal symmetry to derive powerful first-order differential equations for them. Due to on-shell collinear singularities, the Ward identities have an anomaly, which is obtained from lower-loop information. We show that in the five-particle case, the solution to the equations is uniquely fixed by the expected analytic behavior. We apply the method to a non-planar two-loop five-particle integral.
In this paper we study the four-point correlation function of the energy-momentum supermultiplet in theories with N=4 superconformal symmetry in four dimensions. We present a compact form of all component correlators as an invariant of a particular abelian subalgebra of the N=4 superconformal algebra. This invariant is unique up to a single function of the conformal cross-ratios which is fixed by comparison with the correlation function of the lowest half-BPS scalar operators. Our analysis is independent of the dynamics of a specific theory, in particular it is valid in N=4 super Yang-Mills theory for any value of the coupling constant. We discuss in great detail a subclass of component correlators, which is a crucial ingredient for the recent study of charge-flow correlations in conformal field theories. We compute the latter explicitly and elucidate the origin of the interesting relations among different types of flow correlations previously observed in arXiv:1309.1424.
We study holographically Lifshitz-scaling theories with broken symmetries. In order to do this, we set up a bulk action with a complex scalar and a massless vector on a background which consists in a Lifshitz metric and a massive vector. We first study separately the complex scalar and the massless vector, finding a similar pattern in the two-point functions that we can compute analytically. By coupling the probe complex scalar to the background massive vector we can construct probe actions that are more general than the usual Klein--Gordon action. Some of these actions have Galilean boost symmetry. Finally, in the presence of a symmetry breaking scalar profile in the bulk, we reproduce the expected Ward identities of a Lifshitz-scaling theory with a broken global continuous symmetry. In the spontaneous case, the latter imply the presence of a gapless mode, the Goldstone boson, which will have dispersion relations dictated by the Lifshitz scaling.
Basic properties of gauge theories in the framework of Faddeev-Popov (FP) method, Batalin-Vilkovisky (BV) formalism, functional renormalization group approach are considered. The FP- and BV- quantizations are characterized by the BRST symmetry while the BRST symmetry is broken in the FRG approach. It is shown that the FP-method, the BV-formalism and the FRG approach can be provided with the Slavnov-Taylor identity, the Ward identity and the modified Slavnov-Taylor identity respectively. It is proved that using the background field method, the background gauge invariance of effective action within the FP and FRG quantization procedures can be achieved in non-linear gauges. The gauge dependence problem within the FP-, BV- and FRG quantizations is studied. Arguments allowing to state impossibility of gauge independence of physical results obtained within the FRG approach are given.
Since the work of Ryu and Takayanagi, deep connections between quantum entanglement and spacetime geometry have been revealed. The negative eigenvalues of the partial transpose of a bipartite density operator is a useful diagnostic of entanglement. In this paper, we discuss the properties of the associated entanglement negativity and its Renyi generalizations in holographic duality. We first review the definition of the Renyi negativities, which contain the familiar logarithmic negativity as a special case. We then study these quantities in the random tensor network model and rigorously derive their large bond dimension asymptotics. Finally, we study entanglement negativity in holographic theories with a gravity dual, where we find that Renyi negativities are often dominated by bulk solutions that break the replica symmetry. From these replica symmetry breaking solutions, we derive general expressions for Renyi negativities and their special limits including the logarithmic negativity. In fixed-area states, these general expressions simplify dramatically and agree precisely with our results in the random tensor network model. This provides a concrete setting for further studying the implications of replica symmetry breaking in holography.
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